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Continuous Time Wishart Process for Stochastic Risk

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  • C. Gourieroux

Abstract

Risks are usually represented and measured by volatility-covolatility matrices. Wishart processes are models for a dynamic analysis of multivariate risk and describe the evolution of stochastic volatility-covolatility matrices, constrained to be symmetric positive definite. The autoregressive Wishart process (WAR) is the multivariate extension of the Cox, Ingersoll, Ross (CIR) process introduced for scalar stochastic volatility. As a CIR process it allows for closed-form solutions for a number of financial problems, such as term structure of T-bonds and corporate bonds, derivative pricing in a multivariate stochastic volatility model, and the structural model for credit risk. Moreover, the Wishart dynamics are very flexible and are serious competitors for less structural multivariate ARCH models.

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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Econometric Reviews.

Volume (Year): 25 (2006)
Issue (Month): 2-3 ()
Pages: 177-217

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Handle: RePEc:taf:emetrv:v:25:y:2006:i:2-3:p:177-217

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Related research

Keywords: JEL Number; G12; G13;

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Cited by:
  1. Almut Veraart & Luitgard Veraart, 2012. "Stochastic volatility and stochastic leverage," Annals of Finance, Springer, vol. 8(2), pages 205-233, May.
  2. Manabu Asai & Michael McAleer, 2013. "Leverage and Feedback Effects on Multifactor Wishart Stochastic Volatility for Option Pricing," Tinbergen Institute Discussion Papers 13-003/III, Tinbergen Institute.
  3. Manabu Asai & Michael McAleer, 2013. "A Fractionally Integrated Wishart Stochastic Volatility Model," Tinbergen Institute Discussion Papers 13-025/III, Tinbergen Institute.
  4. Manabu Asai & Michael McAleer, 2013. "A Fractionally Integrated Wishart Stochastic Volatility Model," Tinbergen Institute Discussion Papers 13-025/III, Tinbergen Institute.
  5. Takashi Kato & Jun Sekine & Kenichi Yoshikawa, 2013. "Order Estimates for the Exact Lugannani-Rice Expansion," Papers 1310.3347, arXiv.org, revised Jun 2014.
  6. repec:wyi:wpaper:002054 is not listed on IDEAS
  7. Kang, Chulmin & Kang, Wanmo, 2013. "Transform formulae for linear functionals of affine processes and their bridges on positive semidefinite matrices," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 2419-2445.
  8. Siddhartha Chib & Yasuhiro Omori & Manabu Asai, 2007. "Multivariate stochastic volatility (Revised in May 2007, Handbook of Financial Time Series (Published in "Handbook of Financial Time Series" (eds T.G. Andersen, R.A. Davis, Jens-Peter Kreiss," CARF F-Series CARF-F-094, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  9. Gourieroux, C. & Monfort, A., 2008. "Quadratic stochastic intensity and prospective mortality tables," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 174-184, August.
  10. K. Triantafyllopoulos, 2012. "Multi‐variate stochastic volatility modelling using Wishart autoregressive processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(1), pages 48-60, 01.
  11. Gourieroux, Christian & Sufana, Razvan, 2011. "Discrete time Wishart term structure models," Journal of Economic Dynamics and Control, Elsevier, vol. 35(6), pages 815-824, June.
  12. Gourieroux, C. & Jasiak, J. & Sufana, R., 2009. "The Wishart Autoregressive process of multivariate stochastic volatility," Journal of Econometrics, Elsevier, vol. 150(2), pages 167-181, June.
  13. Siddhartha Chib & Yasuhiro Omori & Manabu Asai, 2007. "Multivariate stochastic volatility," CIRJE F-Series CIRJE-F-488, CIRJE, Faculty of Economics, University of Tokyo.
  14. Manabu Asai & Michael McAleer, 2013. "Leverage and Feedback Effects on Multifactor Wishart Stochastic Volatility for Option Pricing," Tinbergen Institute Discussion Papers 13-003/III, Tinbergen Institute.
  15. Asai, Manabu & McAleer, Michael, 2009. "The structure of dynamic correlations in multivariate stochastic volatility models," Journal of Econometrics, Elsevier, vol. 150(2), pages 182-192, June.

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